# DAVV MBA QUESTION PAPERS

Dec 2015

Master of Business Administration (MBA) Examination

I Semester

Mathematics and Statistics for Managers

Time : 3 Hours] [ Max. Marks : 80

Note : Attempt any five. questions with a minimum of two questions from
each section. All questions carry equal marks.

Section A

1. (a) Examine the continuity of the function :

f(x)= |x| + |x-1| + |x-2| at x = 2.

(b) Evaluate :

2.(a) Find the largest and the smallest value of the polynomial x3 –18x2
+96x in the interval [0, 9].

(b) Evaluates Tg approximately by the use of differential.

3.(a) The marginal cost of production of a firm is given by:

C' (x) = (d/dx) C(x) = 5 + 0.13x

The marginal revenue is given as (d/dx) R(x) = R' (x) = 18. The fixed
cost is Rs. 120. Calculate the total (maximum) profit.

(ba) A man borrowed Rs. 20,000 at 6% compound interest promising to
repay Rs, 5,000 at the end of each of the first 4 years to reduce
principal and interest and to pay the balance at the end of 5th year.
Find the amount of his final payment.

4. (a) Find the inverse of the matrix :

1 –1 0

2 3 4

0 1 2

(b) Find the values of a, b and c if the matrix A is given by :

a 2 2

A=(1/3) 2 1 b

2 c 1

and further it obeys the law AA' – I, where A denotes the transpose of A
and I is the unit matrix of order 3.

Section B

5. (a) The chances that doctor A will diagnose a disease X correctly is

60%. The chances that a patient will die by his treatment alter the
correct diagnosis is 40% and the chances of death by wrong diagnosis is
70%. A patient of doctor A, who had disease X died. What is the
probability that his disease was diagnosed correctly ?

(b) Write a note on Normal Distribution and discuss its characteristics.

6. (a) The Spearman's Rank Correlation
between the marks obtained by 10 students in two Subjects A and B was
found to be 0.5. It was later found that the difference in ranks in the
above two subjects obtained by one of the students was wrongly taken as
3 instead of the correct difference 7. Find the correct value of the
rank-correlation.

(b) What do you mean by Regression? Why there are only two regression
lines ? Discuss the properties of the regression coefficients.

7. (a) Write a explanatory note on
different models used in Time Series and discuss its different
components.

(b) Fit a straight line trend by the method of least squares to the
following data. Assuming; that the same rate of change continues, what
would be the predicted earnings for the year 1985 ?

Year :
1976 1977 1978
1979 1980
1981 1982 1983

Sales (Lakh Rs.) : 76 80
130 144
138 120
174 190

8. (a) Discuss the Essential elements
of decision-making problem.

(b) What is decision under risk? Discuss the steps to obtain expected
Monetary Value (EMV) and state its significance.